Properties

Label 88935p
Number of curves $4$
Conductor $88935$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("p1")
 
E.isogeny_class()
 

Elliptic curves in class 88935p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
88935.j3 88935p1 \([1, 1, 1, -14946, 660078]\) \(1771561/105\) \(21884349909345\) \([2]\) \(276480\) \(1.3128\) \(\Gamma_0(N)\)-optimal
88935.j2 88935p2 \([1, 1, 1, -44591, -2814316]\) \(47045881/11025\) \(2297856740481225\) \([2, 2]\) \(552960\) \(1.6594\)  
88935.j4 88935p3 \([1, 1, 1, 103634, -17399656]\) \(590589719/972405\) \(-202670964510444045\) \([2]\) \(1105920\) \(2.0059\)  
88935.j1 88935p4 \([1, 1, 1, -667136, -209997292]\) \(157551496201/13125\) \(2735543738668125\) \([2]\) \(1105920\) \(2.0059\)  

Rank

sage: E.rank()
 

The elliptic curves in class 88935p have rank \(1\).

Complex multiplication

The elliptic curves in class 88935p do not have complex multiplication.

Modular form 88935.2.a.p

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} - q^{4} - q^{5} + q^{6} + 3 q^{8} + q^{9} + q^{10} + q^{12} - 6 q^{13} + q^{15} - q^{16} + 2 q^{17} - q^{18} - 8 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.